Coordinate systems

Review What term can we use to define the true shape and size of the earth? What do we use to in place of this shape because it’s simpler to use? How do we link the two (i.e., link real locations to the ellipsoid)? What are projections used for? Keep in mind that the term “projection change” is often synonymous with changing datum etc. because a GIS treats this as one step

Spatial Location and Reference: Latitude / Longitude Most commonly-used coordinate system Lines of latitude are called parallels Lines of longitude are called meridians Parallels parallel to each other; circle the globe ew Max value of angular measurement N and S from the equator: 90 degrees Meridians: perpendicular to parallels Prime meridian: Greenwich, England Meridians run 180 degrees E and W of the prime meridian (until reach International Date Line)

Latitude / Longitude Prime Meridian & Equator are the reference points used to define latitude and longitude

Latitude and Longitude is a Geographic Coordinate System This is a Global Coordinate System Based on angles on the ellipsoidal Earth latitude positive in n. hemisphere negative in s. hemisphere longitude positive east of Prime Meridian negative west of Prime Meridian Conceptually this is a 2-dimensional, spherical coordinate system, which is actually an oxymoron (since a sphere is a 3D object), but we can effectively use 2 coordinated to define a location with the 3rd coordinate (the z-value) just assumed to be the surface of the earth. Problems with using Lat/Long: 1) A sphere is impossible to turn into a flat surface (like a map) without some distortion – hence our projections lecture 2) People are much more comfortable working with 2D than 3D because our basic understanding of geometry and trigonometry is stronger in 2D 3) Even in GIS it’s easier to work with 2D than 3D, particularly when we remember that someone had to make the GIS software and that computers used to be slow. This is slowly changing and one day we may only worry about projections when it’s time to make a map because all calculations will be done based using 3D coordinates.

The units of measurement in Latitude and Longitude are degrees given as either decimal degrees or degrees, minutes, and seconds e.g., Chapel Hill is 35.913 N, -79.056 W in decimal degrees OR 35° 54’ 47” N, 79° 3’ 22” W in degrees, minutes, seconds

Cartesian Coordinates Computationally, it is much simpler to work with Cartesian coordinates than with spherical coordinates x,y coordinates referred to as “eastings” & “northings” defined units, e.g. meters, feet Cartographers hate negative numbers \ Remember (again) that converting the 3D world into 2D, even for a small area, adds distortion. 2D coordinate systems are tied to projections

Examples Common coordinate systems: Universal Transverse Mercator Applicable nearly world-wide Country-wide coordinate systems: US – the State Plane Coordinate System UK – Ordnance Survey National Grid As with ellipsoids, datums, and projections, there are lots of coordinate systems out there to choose from. Here are a few coordinate systems that convert the, with the use of a projection, convert the world into a set 2D grids

Universal Transverse Mercator (UTM) Coordinate System UTM is a coordinate system that you will use in lab (and beyond this class if you use GIS), so you should know something about it.

UTM Zone Projection Central meridian Standard lines Transverse Mercator: A cylindrical projection 60 zones, each 6° longitude wide to minimize distortion Zones run from 80° S to 84° N Coordinates within each zone must be specified Poles covered by Universal Polar System (UPS) What causes distortion? Where is it the most problematic?

Projection Aspects cylindrical conical planar Recall that transverse means that the standard lines are meridians (lines of longitude) planar

UTM Coordinate Parameters Units = meters N and S zones have separate coordinates Each zone: 6o longitude wide Y-origin: Equator (N zones) near South pole (S zones)* X-origin: 500,000 m west of central meridian Why are poles not included? * Actually, it’s 10,000,000 meters south of the equator

Universal Transverse Mercator Each zone looks like this. North or South must be specified (i.e. we are currently in UTM zone 17N, not just zone 17)

USA In The UTM Zones

UTM What do you do when the area of interest crosses UTM zones? This problem is certain to occur with areas that are wider than 6° of longitude, but on some occasions even a narrower area of interest will happen to be bisected by the edge of a UTM zone All features need to be encoded using a consistent coordinate system  it is customary to assign the coordinates to the more predominant zone that contains the majority of the area of interest

Universal Transverse Mercator Nicaragua

UTM It is also possible to encounter an instance when your area of interest crosses the Equator Northern zone: The Equator’s Northing is at 0m (the Northern zone y-origin is at the Equator) Southern zone: The Equator’s Northing is at 10,000,000m (the Southern zone y-origin is defined as being 10,000,000m south of the Equator) Coordinates must be consistent! 0  10,000,000 The usual solution is to assign all coordinates to the Southern zone

UTM Ecuador

State Plane Coordinate System The State Plane Coordinate System (SPCS) is only defined and used in the United States Like UTM, it is divided into zones, but here zones are fully contained within states Some larger states contain multiple zones Original units are feet, many states are now switching to meters

Map Projections for State Plane Coordinate System E-W zones: Lambert conformal conic projection N-S zones: Transverse Mercator Projection

Lambert Conformal Conic Most states that are spread east to west use this projection. The Lambert Conformal Conic projection does not use a single latitude line as its point of contact (a standard line). Instead, the earth's surface intersects the cone along two lines, called secants. Along these two lines there is no distortion, but distortion does occur as the distance from the secants increases.

Lambert Conformal Conic                                                                                                                                                         Distortion increases as you move away from the secant (standard) lines

SPCS The origin for each zone is placed outside the zone to the southwest (a false origin) X-origin: Transverse Mercator (N-S) Zones ~ 500,000 feet west of the furthest point west Lambert Conformal Conic (E-W) Zones ~ 2,000,000 feet west of the furthest point west Y-origin is not a specific distance to the south (varies by state and zone)

UTM vs SPCS SPCS UTM More accurate than UTM used primarily for engineering applications, e.g. utility companies, local governments to do accurate surveying of facilities network (sewers, power lines) Used for small areas Difficult to use over larger areas (when multiple zones are necessary) UTM allows overlap between zones for mapping purposes The UTM system is global In general, state plane was designed so that people working in a relatively small area (like a state or a part of a state) would not have to take the curvature of the earth into account when surveying (again, because 2-D is easier to work with, particularly in the field)

Spatial Location and Reference Communicating the location of objects Absolute location Definitive, measurable, fixed point in space Relative location Location determined relative to other objects in geographic space Can you give example coordinate systems for each? Absolute location = Latitude/Longitude Relative locations = UTM or state plane

Class Survey Please take a piece of paper and write answers to the following questions 1) What do you like about this class? 2) What would you change if you could? I’m asking now so things can potentially change if there is a problem…. Unlike with a survey at the end of the semester. Probably should ask this after lectures on things like geodesy, datums, and projections (really, it gets better, I promise).